Comparing speeds

What is the speed benefit of this perfect hashtable compared to
HashMap? I'll test the two by comparing
PerfectHashMaps to HashMaps which have the
benefit of the same amount of memory, as well as measurements against
a HashMap sized to just contain the set. I've optimized
the Key.hashCode() and key.equals() methods
so that the HashMaps are not at a disadvantage from these
methods. And I've included a test against a KeyHashMap
implementation, a specialized implementation of HashMap,
which is optimized for Key object keys (see "Optimizing a
query on a Map" in the resource section below).

It is worth noting that the HashMap.put() method
performs at different speeds depending on whether or not the
put() is overwriting an existing entry. With no existing
entry for a key, the HashMap needs to create a node
element before inserting the value into the collection, whereas the
node already exists when the entry is being overwritten. So I test
both these scenarios too. All measured times have been scaled by the
same value for simpler comparison.

Table 5: Comparing the performance of various Maps using the put() method on an empty table

Table 6: Comparing the performance of various Maps using the put() method on a full table

put() overwriting previous element at key

1.2 JVM

1.3 JVM

HotSpot 2.0

1

HashMap, size of key set

17.4%

21.9%

27.7%

2

HashMap, same size as perfect hash map

18.3%

24.1%

18.6%

3

KeyHashMap, size of key set

13.4%

17.0%

15.4%

4

KeyHashMap, same size as perfect hash map

14.6%

16.1%

15.5%

5

PerfectKeyHashMap

15.15

14.0%

11.4%

6

MinimalPerfectKeyHashMap (size of key set)

32.4%

34.3%

27.2%

Table 7: Comparing the performance of various Maps using the get() method

get()

1.2 JVM

1.3 JVM

HotSpot 2.0

1

HashMap, size of key set

16.6%

25.1%

20.6%

2

HashMap, same size as perfect hash map

17.1%

20.4%

16.8%

3

KeyHashMap, size of key set

13.4%

11.7%

12.6%

4

KeyHashMap, same size as perfect hash map

13.2%

15.1%

11.7%

5

PerfectKeyHashMap

7.3%

8.7%

6.6%

6

MinimalPerfectKeyHashMap (size of key set)

16.0%

18.2%

14.9%

The comparisons show that PerfectKeyHashMap can be
significantly faster than any of the other implementations except in
the case where a put() is overwriting an existing
entry. The Maps based on the HashMap
function have a severely decreased worst case performance, which
occurs when many of the keys map to the same index (not tested here),
whereas the PerfectKeyHashMap has constant performance
independent of the key set.

Reducing excessive memory requirements

Our hash function may require a large table in the worst case. A
useful concept is the memory factor requirement of the
perfect maps, which I define as the number of times larger the memory
needs to be compared to the number of elements being stored in the
maps. For the examples previously listed, the set {keys 1}
using the hash function %7 produced a memory factor requirement of
1.75 (four elements requiring seven indexes); {keys 2} using
%3 produced a memory factor requirement of 1; {keys 3} using
%14 produced a memory factor requirement of 3.

I ran a test of thousands of randomly generated keysets of between
5 and 500 elements where each key value was retricted to the range 1
to 10,000. This test produced an average memory factor requirement of
12 and a maximum factor of 20. Whether these memory requirements are
reasonable for your application depends on how many large perfect maps
you need to create and on the importance of speed compared to
memory. Can we gain the benefits of the perfect map without the large
memory overhead?

For some datasets it may be possible to produce a perfect hash
function that is fast and has a small memory factor requirement (for
example the final map implementation in the article "Optimizing a
query on a Map"). In general, however, reducing the memory overhead of
hash functions usually requires the use of a table, thus reducing the
speed of the hash function.

For the hash functions considered in this article, we have the
required tables available already; the perfect maps provide us with
tables that can produce minimal perfect maps. Since any minimal
perfect map requires a perfect map as well, you may think we have
increased the memory requirements rather than reduced
them. But multiple minimal perfect map instances for the same set of
keys can all point to the same perfect map for their memory map table;
therefore, depending on the application, this might be a feasible
solution. The optimized implementation of the
MinimalPerfectKeyHashMap looks like

Examples of minimal perfect map usage can be found in the
associated source code with this article. However, the speed tests
applied to the minimal perfect map (the rows numbered 6, in tables 5
through 7) show that there may be no advantage to using this
implementation of MinimalPerfectKeyHashMaps. The table
lookup produces enough of an overhead that an optimized
KeyHashMap using the HashMap function can
produce superior performance.